Abstract:

Compressive sensing (CS) also known as compressive sampling is a technique used to reconstruct or recover the full-length of a signal with only a few non-adaptive measurements. It is a model-based framework for data acquisition and signal recovery that is based on the principles of sparsity and incoherence. Sparsity refers to the fact that a signal of interest is sparse and compressible and can be represented concisely in a given basis. Incoherence refers to the idea that a sparse signal is spread out in the basis in which it is acquired. A prominent area of application of this technique is tomography such as magnetic resonance imaging (MRI), X-ray CT, and in 3D synthetic aperture radar (SAR) imaging for reconstructing the elevation reflectivity profile.

This dissertation describes the investigation into three-dimensional (3D) synthetic aperture sonar (SAS) imaging in air using compressive sampling. In the work, a 3D SAS simulator using compressive sampling was implemented in MATLAB. The effect of the number of baselines as well as the super-resolution factor on the final image was also investigated. A real 3D SAS imaging system was designed and the results were compared with the results of the simulated system.

In the system, the SAS data was captured in a multiple transducer (baseline), single-pass configuration with 15 ultrasonic receivers and a single ultrasonic transmitter that operate at about 40 kHz. Signal conditioning circuits for the transmit and receive signals were built on pieces of veroboard. A PC which ran a custom designed LabVIEW virtual instrument (VI) was used for the synchronous transmission and reception of ultrasonic signals, and the control of the SAS platform via the NI PCI-6070E data acquisition card. The received 2D SAS signal from each transducer was focused using the accelerated chirp scaling algorithm. Compressive sensing was applied to a stack of focused 2D SAS images to achieve focusing in the elevation direction. 3D scenes containing point targets were successfully reconstructed in 3D SAS images using this technique with 9 baselines and a super-resolution factor of 3.

The results confirm that CS is an effective technique in super-resolution tomographic reconstructions provided the baseline span is small compared to the imaging range. Also for reliable reconstructions, the appropriate super-resolution factor and number of acquisitions must be chosen.